Journal of Applied and Industrial Mathematics最新文献

The following game of two persons is formalized and solved in the paper. Player 1 is askeda question. Player 2 knows the correct answer. Moreover, both players know all possible answersand their a priori probabilities. Player 2 must choose a subset of the given cardinality of deceptionanswers. Player 1 chooses one of the proposed answers. Player 1 wins one from Player 2 if he/sheguessed the correct answer and zero otherwise. This game is reduced to a matrix game. However,the game matrix is of large dimension, so the classical method based on solving a pair of duallinear programming problems cannot be implemented for each individual problem. Therefore, it isnecessary to develop a method to radically reduce the dimension.

The whole set of such games is divided into two classes. The superuniform class ofgames is characterized by the condition that the largest of the a priori probabilities is greater thanthe probability of choosing an answer at random, and the subuniform class corresponds to theopposite inequality—each of the a priori probabilities when multiplied by the total numberof answers presented to Player 1 does not exceed one. For each of these two classes, the solvingthe extended matrix game is reduced to solving a linear programming problem of a much smallerdimension. For the subuniform class, the game is reformulated in terms of probability theory. Thecondition for the optimality of a mixed strategy is formulated using the Bayes theorem. For thesuperuniform class, the solution of the game uses an auxiliary problem related to the subuniformclass. For both classes, we prove results on the probabilities of guessing the correct answer whenusing optimal mixed strategies by both players. We present algorithms for obtaining thesestrategies. The optimal mixed strategy of Player 1 is to choose an answer at random in thesubuniform class and to choose the most probable answer in the superuniform class. Optimalmixed strategies of Player 2 have much more complex structure.

The paper proposes a fractional-differential modification of the mathematical model of theprocess of nonstationary charging of polar dielectric materials under conditions of irradiation withmedium-energy electron beams. The mathematical formalization is based on a sphericallysymmetric diffusion–drift equation with a fractional time derivative. An implicit finite-differencescheme is constructed using the Caputo derivative approximation. An application program hasbeen developed in Matlab softwarethat implements the designed computational algorithm. Verification of an approximate solution ofthe problem is demonstrated using a test example. The results of computational experiments toevaluate the characteristics of field effects of injected charges in ferroelectrics when varying theorder of fractional differentiation in subdiffusion regimes are presented.

We consider an approach to solving permutation scheduling problems using graphicsaccelerators. A parallel evolutionary algorithm based on the iterated random local search and the“Go with the winners” algorithm is proposed. A computational experiment was carried out on testinstances of the classic Flow Shop problem and one applied production scheduling problem withtime windows. The results show high computing speed and good accuracy of obtained solutions incomparison with various variants of the genetic algorithm and Gurobi solver. The proposedapproach is easy to implement and convenient for adaptation to particular features of graphicscomputing and can be used to solve practical problems.

We consider an initial–boundary value problem for quasilinear equations of complex heattransfer that model the process of endovenous laser ablation. A priori estimates for the solutionare obtained. Results on the global unique solvability of the problem are presented. An algorithmfor finding a solution of the initial–boundary value problem is proposed. The efficiency of thealgorithm is illustrated by numerical examples. The influence of internal thermal radiation on thebehavior of temperature fields is evaluated.

The paper studies the properties of the set of numbers smaller than and coprime to( n ) with the modulo( n ) multiplication operation introduced on it (this object is sometimes called theEuler group). The cardinality of such a set is the well-known Euler function( varphi (n) ), which is one of the classical functions in the number theory. The fields of itsapplication are quite wide and include, for example, various branches of discrete mathematics, andit also has significant applications in cryptography. The paper considers various combinatorialproblems arising in the study of the Euler group and the Euler function. Relations betweentheoretical and numerical parameters associated with the Euler group and Euler function arederived. The combinatorial relations obtained in the paper can be used when solving appliedcombinatorial problems and in cryptography.

For a given graph, the edge-coloring problem is to minimize the number of colors sufficientto color all the graph edges so that any adjacent edges receive different colors. For all classesdefined by sets of forbidden subgraphs, each with 7 edges, the complexity status of this problem isknown. In this paper, we obtain a similar result for all sets of 8-edge prohibitions.

The evolution of the wave pattern in a multimodulus elastic half-space with a boundarymoving in nonstationary uniaxial piecewise linear “tension–compression–stop” mode is studied.The solution of the boundary value problem includes all cases of interaction between planeone-dimensional strain waves, including reflected weak-intensity fronts. A number of new featuresof one-dimensional elastic deformation dynamics in a multimodulus medium are revealed, some ofwhich (e.g., the appearance of a reflected shock wave at a distance from the loaded boundary,cyclic transitions of a narrow moving zone from a compressed to rigid state and back, and astepwise decrease in the tensile strain level in the near-boundary zone after the boundary isstopped) can be obtained with a given boundary loading only taking into account reflectioneffects.

The problem of steady barotropic motion of a multicomponent medium consisting ofviscous compressible fluids in a bounded domain of three-dimensional space is formulated. Theviscosity matrices are assumed to be arbitrary (nondiagonal). The solvability of a regularized(approximate) problem is proved.

The paper presents the results of mathematical modeling of plasma transfer in a helicalmagnetic field using new experimental data obtained at the SMOLA trap created at the BudkerInstitute of Nuclear Physics of the Siberian Branch of the Russian Academy of Sciences. Plasma isconfined in the trap by transmitting a pulse of magnetic field with helical symmetry to therotating plasma. The mathematical model is based on a stationary plasma transfer equation inthe axially symmetric formulation. The distribution of the concentration of the substanceobtained by numerical simulation confirmed the confinement effect obtained in the experiment.The dependences of the integral characteristics of the substance on the depth of magnetic fieldcorrugation and on plasma diffusion and potential are obtained. The numerical implementationsof the model by the relaxation method and by the Seidel method are compared.

We study the system of equations obtained on the basis of the relativisticSchrödinger equation and relating the potential, amplitude, and phase functions. Usingthe methods of the theory of consistency of systems of partial differential equations, we obtaincompletely integrable systems that relate only two functions of the above three. The systemsfound are related by Bäcklund transformations.